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Encyclopedia > ISO week date

The ISO week date system is a leap week calendar system that is part of the ISO 8601 date and time standard. The system is used (mainly) in government and business for fiscal years, as well as in timekeeping. The leap week calendar is a reformed calendar system with a whole number of weeks every year, and with every year starting on the same weekday. ... ISO 8601, Data elements and interchange formats – Information interchange – Representation of dates and times is an international standard for date and time representations. ... Wall Street, Manhattan is the location of the New York Stock Exchange and is often used as a symbol for the world of business. ...


The system uses the same cycle of 7 weekdays as the Gregorian calendar. Weeks start with Monday. ISO years have a year numbering which is approximately the same as the Gregorian years, but not exactly (see below). An ISO year has 52 or 53 full weeks (364 or 371 days). The extra week is called a leap week, a year with such a week a leap year. This article or section does not cite its references or sources. ... Year numbering is the assignment of integers to calendar years for the purpose of naming the years. ... A leap year (or intercalary year) is a year containing an extra day, week or month in order to keep the calendar year in sync with an astronomical or seasonal year. ...


A date is specified by the ISO year in the format YYYY, a week number in the format ww prefixed by the letter W, and the weekday number, a digit d from 1 through 7, beginning with Monday and ending with Sunday. For example, 2006-W52-7 (or in its most compact form 06W527) is the Sunday of the 52nd week of 2006. In the Gregorian system this day is called 31 December 2006.


The system has a 400-year cycle of 146,097 days (20,871 weeks), with an average year length of exactly 365.2425 days, just like the Gregorian calendar. Since non-leap years have 52 weeks, in every 400 years there are 71 leap years.

Contents


Relation with the Gregorian calendar

The ISO year number deviates from the number of the Gregorian year on, if applicable, a Friday, Saturday, and Sunday, or a Saturday and Sunday, or just a Sunday, at the start of the Gregorian year (which are at the end of the previous ISO year) and a Monday, Tuesday and Wednesday, or a Monday and Tuesday, or just a Monday, at the end of the Gregorian year (which are in week 01 of the next ISO year). In the period 4 January–28 December and on all Thursdays the ISO year number is always equal to the Gregorian year number.


Mutually equivalent definitions for week 01 are:

  • the week with the year's first Thursday in it
  • the week with the year's first working day in it (if Saturdays, Sundays, and 1 January are no working days)
  • the week with January 4 in it
  • the first week with the majority (four or more) of its days in the starting year
  • the week starting with the Monday in the period 29 December - 4 January
  • the week with the Thursday in the period 1 - 7 January
  • If 1 January is on a Monday, Tuesday, Wednesday or Thursday, it is in week 01. If 1 January is on a Friday, Saturday or Sunday, it is in week 52 or 53 of the previous year.

Note that while most definitions are symmetric with respect to time reversal, one definition in terms of working days happens to be equivalent.


The last week of the ISO year is the week before week 01; in accordance with the symmetry of the definition, equivalent definitions are:

  • the week with the year's last Thursday in it
  • the week with December 28 in it
  • the last week with the majority (four or more) of its days in the ending year
  • the week starting with the Monday in the period 22 - 28 December
  • the week with the Thursday in the period 25 - 31 December
  • the week ending with the Sunday in the period 28 December - 3 January
  • If 31 December is on a Monday, Tuesday, or Wednesday, it is in week 01, otherwise in week 52 or 53.

The following years have 53 weeks:

  • years starting with Thursday
  • leap years starting with Wednesday

Examples:

  • 2006-01-01 is 2005-W52-7
  • 2006-01-02 is 2006-W01-1
  • 2006-12-31 is 2006-W52-7
  • 2007-01-01 is 2007-W01-1 (both years 2007 start with the same day)
  • 2007-12-30 is 2007-W52-7
  • 2007-12-31 is 2008-W01-1
  • 2008-01-01 is 2008-W01-2 (Gregorian year 2008 is a leap year, ISO year 2008 is 2 days shorter: 1 day longer at the start, 3 days shorter at the end)
  • 2008-12-29 is 2009-W01-1
  • 2008-12-31 is 2009-W01-3
  • 2009-01-01 is 2009-W01-4
  • 2009-12-31 is 2009-W53-4 (ISO year 2009 is a leap year, extending the Gregorian year 2009, which starts and ends with Thursday, at both ends with three days)
  • 2010-01-03 is 2009-W53-7

The system does not need the concept of month and is not well connected with the Gregorian system of months: some months January and December are divided over two ISO years.


Week number

Overview of dates in common years with a fixed week number:

January January 4th, 11th, 18th, & 25th  wk 1-4
February February 1st, 8th, 15th, & 22nd  wk 5-8
March March 1st, 8th, 14th, 22nd, & 29th  wk 9-13
April April 5th, 12th, 19th, & 26th  wk 14-17
May May 3rd, 10th, 17th, 24th, & 31st  wk 18-22
June June 7th, 14th, 21st, & 28th  wk 23-26
July July 5th, 12th, 19th, & 26th  wk 27-30
August August 2nd, 9th, 16th, 23rd, & 30rd  wk 31-35
September September 6th, 13rd, 20th, & 27th  wk 36-39
October October 4th, 11st, 18th, 25th  wk 40-43
November November 1st, 8th, 15th, 22nd, & 29th  wk 44-48
December December 6th, 13th, 20th, & 27th  wk 49-52

These dates are one day after the Doomsdays. In leap years the week number is the rank number of its Doomsday. January 4 is the 4th day of the year in the Gregorian calendar. ... January 11 is the 11th day of the year in the Gregorian calendar. ... January 18 is the 18th day of the year in the Gregorian calendar. ... January 25 is the 25th day of the year in the Gregorian calendar. ... February 1 is the 32nd day of the year in the Gregorian Calendar. ... February 8 is the 39th day of the year in the Gregorian Calendar. ... February 15 is the 46th day of the year in the Gregorian Calendar. ... February 22 is the 53rd day of the year in the Gregorian Calendar. ... March 1 is the 60th day of the year in the Gregorian calendar (61st in leap years). ... March 8 is the 67th day of the year in the Gregorian Calendar (68th in Leap years). ... March 14 is the 73rd day of the year in the Gregorian Calendar (74th in leap years) with 292 days remaining in the year. ... March 22 is the 81st day of the year in the Gregorian Calendar (82nd in Leap years). ... March 29 is the 88th day of the year in the Gregorian Calendar (89th in Leap years). ... April 5 is the 95th day of the year in the Gregorian calendar (96th in leap years). ... April 12 is the 102nd day of the year in the Gregorian calendar (103rd in leap years). ... April 19 is the 109th day of the year in the Gregorian calendar (110th in leap years). ... April 26 is the 116th day of the year in the Gregorian Calendar (117th in leap years). ... May 3 is the 123rd day of the year in the Gregorian calendar (124th in leap years). ... May 10 is the 130th day of the year in the Gregorian Calendar (131st in leap years). ... May 17 is the 137th day of the year in the Gregorian Calendar (138th in leap years). ... May 24 is the 144th day of the year in the Gregorian calendar (145th in leap years). ... May 31 is the 151st day of the year in the Gregorian calendar (152nd in leap years), with 214 days remaining. ... June 7 is the 158th day of the year in the Gregorian calendar (159th in leap years), with 207 days remaining. ... June 14 is the 165th day of the year in the Gregorian calendar (166th in leap years), with 200 days remaining. ... June 21 is the 172nd day of the year (173rd in leap years) in the Gregorian calendar, with 193 days remaining. ... June 28 is the 179th day of the year (180th in leap years) in the Gregorian Calendar, with 186 days remaining. ... July 5 is the 186th day of the year (187th in leap years) in the Gregorian Calendar, with 179 days remaining. ... July 12 is the 193rd day (194th in leap years) of the year in the Gregorian Calendar, with 172 days remaining. ... July 19 is the 200th day (201st in leap years) of the year in the Gregorian Calendar, with 165 days remaining. ... July 26 is the 207th day (208th in leap years) of the year in the Gregorian Calendar, with 158 days remaining. ... August 2 is the 214th day of the year in the Gregorian Calendar (215th in leap years), with 151 days remaining. ... August 9 is the 221st day of the year in the Gregorian Calendar (222nd in leap years), with 144 days remaining. ... August 16 is the 228th day of the year (229th in leap years) in the Gregorian Calendar. ... This is the song that never ends yes it gos on and on my friends some people started singing it not knowing what it was they just started singing it forever just becauseThis is the song that never ends yes it gos on and on my friends some... August 30 is the 242nd day of the year in the Gregorian Calendar (243rd in leap years), with 123 days remaining. ... This article is about the day of the year. ... September 13 is the 256th day of the year (257th in leap years). ... September 20 is the 263rd day of the year (264th in leap years). ... September 27 is the 270th day of the year (271st in leap years) in the Gregorian calendar, with 95 days remaining. ... October 4 is the 277th day of the year (278th in leap years) in the Gregorian Calendar. ... October 11 is the 284th day of the year (285th in leap years). ... October 18 is the 291st day of the year (292nd in leap years). ... October 25 is the 298th day of the year (299th in leap years) in the Gregorian Calendar, with 67 days remaining. ... November 1 is the 305th day of the year (306th in leap years) in the Gregorian Calendar, with 60 days remaining. ... November 8 is the 312th day of the year (313th in leap years) in the Gregorian Calendar, with 53 days remaining. ... November 15 is the 319th day of the year (320th in leap years) in the Gregorian Calendar, with 46 days remaining. ... November 22 is the 326th day (327th on leap years) of the year in the Gregorian calendar. ... November 29 is the 333rd (in leap years the 334th) day of the year in the Gregorian Calendar. ... December 6 is the 340th day (341st on leap years) of the year in the Gregorian calendar. ... December 13 is the 347th day of the year (348th in leap years) in the Gregorian calendar. ... December 20 is the 354th day of the year (355th in leap years) in the Gregorian calendar. ... December 27 is the 361st day of the year in the Gregorian Calendar (362nd in leap years). ... For any year, Doomsday is the day of the week on which the last day of February falls. ...


Advantages

  • The date directly tells the weekday.
  • All years start with a Monday and end with a Sunday.
  • When used by itself without using the concept of month, all years are the same except that leap years have a leap week at the end.
  • The weeks are the same as in the Gregorian calendar.

Disadvantages

Each equinox and solstice varies over a range of at least seven days. This is because each equinox and solstice may occur any day of the week and hence on at least seven different ISO week dates. For example, there are summer solstices on 2004-W12-7 and 2010-W11-7. The equinoxes are two opposite points on the celestial sphere where the celestial equator and ecliptic intersect. ... Diagram of the Earths seasons Solstice is an astronomical term regarding the position of the Sun in relation to the earths equator. ...


The leap year cycle

Below is the 400-year cycle of years in terms of the dominical letter of the year as shown on the right. The three types of week leap year are D, DC, and ED. The days of the year are sometimes designated letters A, B, C, D, E, F and G in a cycle of 7 as an aid for finding the day of week of a given calendar date and in calculating Easter. ...

Dominical
letter
Doomsday
A or BA Tuesday
B or CB Monday
C or DC Sunday
D or ED Saturday
E or FE Friday
F or GF Thursday
G or AG Wednesday
 ,----,----,----,----, |1600|1700|1800|1900| |2000|2100|2200|2300| ,-----------+----+----+----+----| | 00| BA | C | E | G | |-----------+----+----+----+----| |85 57 29 01| G | B |<D> | F | |86 58 30 02| F | A | C | E | |87 59 31 03| E | G | B |<D> | |88 60 32 04|<DC>| FE | AG | CB | |-----------+----+----+----+----| |89 61 33 05| B |<D> | F | A | |90 62 34 06| A | C | E | G | |91 63 35 07| G | B |<D> | F | |92 64 36 08| FE | AG | CB |<ED>| |-----------+----+----+----+----| |93 65 37 09|<D> | F | A | C | |94 66 38 10| C | E | G | B | |95 67 39 11| B |<D> | F | A | |96 68 40 12| AG | CB |<ED>| GF | |-----------+----+----+----+----| |97 69 41 13| F | A | C | E | |98 70 42 14| E | G | B |<D> | |99 71 43 15|<D> | F | A | C | | 72 44 16| CB |<ED>| GF | BA | |-----------+----+----+----+----| | 73 45 17| A | C | E | G | | 74 46 18| G | B |<D> | F | | 75 47 19| F | A | C | E | | 76 48 20|<ED>| GF | BA |<DC>| |-----------+----+----+----+----| | 77 49 21| C | E | G | B | | 78 50 22| B |<D> | F | A | | 79 51 23| A | C | E | G | | 80 52 24| GF | BA |<DC>| FE | |-----------+----+----+----+----| | 81 53 25| E | G | B |<D> | | 82 54 26|<D> | F | A | C | | 83 55 27| C | E | G | B | | 84 56 28| BA |<DC>| FE | AG | '-----------+----+----+----+----| |1600|1700|1800|1900| |2000|2100|2200|2300| '----'----'----'----' 


Thus the ISO leap years in one 400-year cycle are (with this time the 28-year subcycles arranged horizontally): The doomsday rule or doomsday algorithm is a way of calculating the day of the week of a given date. ...

 D ED D DC D 
 1903 1908 1914 1920 1925 1931 1936 1942 1948 1953 1959 1964 1970 1976 1981 1987 1992 1998 2004 2009 2015 2020 2026 2032 2037 2043 2048 2054 2060 2065 2071 2076 2082 2088 2093 2099 2105 2111 2116 2122 2128 2133 2139 2144 2150 2156 2161 2167 2172 2178 2184 2189 2195 2201 2207 2212 2218 2224 2229 2235 2240 2246 2252 2257 2263 2268 2274 2280 2285 2291 2296 

There are 13 28-year subcycles with 5 leap years each, and 6 remaining leap years in the remaining 36 years (the absence of leap days in the Gregorian calendar in 2100, 2200, and 2300 interrupts the subcycles). The leap years are 27 times 5 years apart, 43 times 6 years, and once 7 years. (A slightly more even distribution would be possible: 26 times 5 years apart, and 45 times 6 years.)


The Gregorian years corresponding to the 71 ISO leap years can be subdivided as follows:

Thus 27 ISO years are 5 days longer than the corresponding Gregorian year, and 44 are 6 days longer. Of the other 329 Gregorian years (neither starting nor ending with Thursday), 70 are Gregorian leap years, and 259 are non-leap years, so 70 ISO years are 2 days shorter, and 259 are 1 day shorter. This is a calendar for any leap year starting on Thursday (dominical letter DC), e. ... This is the calendar for any leap year starting on Wednesday (dominical letter ED), e. ... This is the calendar for any common year starting on Thursday (dominical letter D). ...


Other week numbering systems

For an overview of week numbering systems see week number. The US system has weeks from Sunday through Saturday, and partial weeks at the beginning and the end of the year. An advantage is that no separate year numbering like the ISO year is needed, while correspondence of lexicographical order and chronological order is preserved. A week is a [ PER [unit]] of time longer than a day and shorter than a month. ...


See also

  • ISO week date

External links


 
 

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